Physics 2220 (Schroeder)
Electrostatics Study Guide
You should understand the basic properties of electric charge, including the two types of charge,
induced charges, charge conservation, conductors, and insulators.
Coulomb’s law for the electrostatic force:
|~
Fe|=K|q1q2|
r2, K =1
4π≤0
= 8.99 ×109N·m2
C2.
Definition of the electric field: ~
E(x, y, z)≡~
Fon q0/q0,
where q0is any “test charge” that you could hypothetically put at the point (x, y, z ).
Field created by a point charge:
|~
Eof Q|=K|Q|
r2.
For more complicated sources, the field is the vector sum of the individual fields (“principle of
superposition”). You should be able to draw qualitatively accurate sketches of electric fields for
various situations, especially those involving symmetry.
Definition of flux:
Φ=|~
E|Acos θ,
summed over pieces of the surface if necessary. For a closed surface, outward fluxes are positive,
inward fluxes are negative. Gauss’s law says that
total flux of ~
Ethrough closed surface = 4πKQinside =Qinside
≤0
.
Properties of conductors in equilibrium: ~
E= 0 inside; ~
Eis perpendicular to surface outside; all
excess charge is on the surface, and tends to concentrate around sharp points.
Definition of voltage (potential):
V(x, y, z) = Ue/q0,
where q0is any “test charge” that you could hypothetically put at the point (x, y, z ). Like the
potential energy Ue, the voltage is always relative to some arbitrary reference point (“ground”).
If the source is a single point charge Qand the reference point is at infinity, then U=KQq0/r.
For a proton, q0= 1.6×10−19 C; the charge of an electron is the same size but negative. An
“electron-volt” (eV) is a unit of energy equal to 1.6×10−19 J.
Relation between Vand ~
E:
∆V=−~
E·~
dr.
In other words, ~
Epoints from high voltage to low voltage, and the magnitude |~
E|is the change in
voltage per unit distance as you move in that direction.
A capacitor is a device that stores positive charge Qand negative charge −Q, separated from each
other, when a voltage difference ∆Vis applied. The capacitance is defined as
C=Q/∆V ,
charge per unit voltage. The simplest capacitor consists of two parallel plates separated by a small
gap. Using the formula for the field near a plane of charge, you can show that in this case the
capacitance is ≤0A/d, where Ais the plate area and dis the separation.